# Degrees to Radians (° to rad)

> Convert degrees to radians: 1 ° = 0.0174533 rad. Exact conversion factor, formula, 22-row table and worked examples, with JSON API and MCP access.

- Page id: `degrees-to-radians` · Quantity: Angle (`angle`, base unit rad) · Tool: `convert_units`
- Canonical page: https://tttkmbb.com/conversion/degrees-to-radians · This document: https://tttkmbb.com/conversion/degrees-to-radians.md · JSON: https://tttkmbb.com/conversion/degrees-to-radians.json (add `?value=` for a result)

## Formula

- `1 ° = 0.0174533 rad`
- `radians = degrees × 0.01745329252`
- Reverse: `degrees = radians × 57.29577951`

The factor follows from the SI definitions of both units (NIST SP 811); values below are rounded to 6 significant figures, the API returns up to 12.

## Worked examples

- 5 ° = 0.0872665 rad
- 12.5 ° = 0.218166 rad
- 100 ° = 1.74533 rad

## Conversion table

| Degrees (°) | Radians (rad) |
| --- | --- |
| 1 | 0.0174533 |
| 2 | 0.0349066 |
| 3 | 0.0523599 |
| 4 | 0.0698132 |
| 5 | 0.0872665 |
| 6 | 0.10472 |
| 7 | 0.122173 |
| 8 | 0.139626 |
| 9 | 0.15708 |
| 10 | 0.174533 |
| 15 | 0.261799 |
| 20 | 0.349066 |
| 25 | 0.436332 |
| 30 | 0.523599 |
| 40 | 0.698132 |
| 50 | 0.872665 |
| 75 | 1.309 |
| 100 | 1.74533 |
| 200 | 3.49066 |
| 250 | 4.36332 |
| 500 | 8.72665 |
| 1000 | 17.4533 |

## API

- `GET https://tttkmbb.com/api/v1/convert?value=5&from_unit=deg&to_unit=rad` → unified JSON envelope with `result.values.result`, `formula`, `factor`, `sources`, `freshness`
- MCP: server `https://tttkmbb.com/mcp`, tool `convert_units` with `{"value":5,"from_unit":"deg","to_unit":"rad"}`
- All angle units: https://tttkmbb.com/api/v1/units?quantity=angle · full converter: [Angle Converter](https://tttkmbb.com/conversion/angle.md)
- Authentication: none. Freshness: `static` (fixed conversion factors).

## FAQ

**How many radians are in one degree?**

1 ° = 0.0174533 rad. The factor comes from the SI definitions of both units (NIST SP 811 / BIPM), so it is exact or correct to at least 10 significant figures.

**What is the formula to convert degrees to radians?**

Multiply the value in degrees by 0.01745329252: radians = degrees × 0.01745329252. For example, 5 ° = 0.0872665 rad.

**How do I convert radians back to degrees?**

Multiply by the inverse factor 57.29577951 (degrees = radians × 57.29577951), or use the radians-to-degrees page.

## Related conversions

- [Radians to degrees](https://tttkmbb.com/conversion/radians-to-degrees.md) (reverse)
- [Gradians to Degrees](https://tttkmbb.com/conversion/gradians-to-degrees.md)
- [Degrees to Gradians](https://tttkmbb.com/conversion/degrees-to-gradians.md)
- [Turns (revolutions) to Degrees](https://tttkmbb.com/conversion/turns-to-degrees.md)
- [Degrees to Turns (revolutions)](https://tttkmbb.com/conversion/degrees-to-turns.md)
- [Arcminutes to Degrees](https://tttkmbb.com/conversion/arcminutes-to-degrees.md)
- [Degrees to Arcminutes](https://tttkmbb.com/conversion/degrees-to-arcminutes.md)
- [Milliradians to Degrees](https://tttkmbb.com/conversion/milliradians-to-degrees.md)
- [Degrees to Milliradians](https://tttkmbb.com/conversion/degrees-to-milliradians.md)

## Data Sources

- NIST Special Publication 811 – Guide for the Use of the International System of Units (SI), Appendix B conversion factors — https://www.nist.gov/pml/special-publication-811 (standard, retrieved 2026-09-24)
- BIPM – The International System of Units (SI Brochure, 9th edition) — https://www.bipm.org/en/publications/si-brochure (standard, retrieved 2026-09-24)
- Wikipedia – Conversion of units — https://en.wikipedia.org/wiki/Conversion_of_units (reference, retrieved 2026-09-24)